Accessibility as a determinant of retail sales

V

ACCESSIBILITY AS A DETERMINANT OF RETAIL SALES by ROBERT BREUER

B.C.E., Polytechnic Institute of Brooklyn (1957)

SUBMITTED IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE

DEGREE OF MASTER OF CITY PLANNING at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June, 1962 Signature of Author:

Department of City apd Regionl Planning, May 18, 1962 Certified by:

Accepted by:

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

GRADUATE THESIS SUBJECT HEADINGS

(To be submitted to Department Headquarters with the original copy of the graduate thesis for transmission to the Library) Author I ET BREDER First Co-Author(s) Thesis Title Last ACCESSIBILITY

Middle Full names

as appearing on Diploma First Middle

AS A DETEEMINANT OF RETAIL SALES

Submitted to the Department of CMITZM Rmon P=I7AL1=4-TN For the Degree of

Date Degree Expected

MASTER OF CITY PLANNING JUNE 1962

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Subject Headings ACCESSIBILITY FORMUALE

RETAIL COMPZTITION

Date ~ /9'> 2

r3

ABSTRACT

ACCESSIBILITY AS A DETERMINANT OF RETAIL SALES

by

ROBERT BREUER

Submitted to the Department of City and Regional Planning on May 18,.1962, in partial fulfillment of' the requirements for the degree of Master of City Planning.

The relationship between accessibility and the spatial distribution of urban activities and their interactions has received widespread interest from urban planners, but few attempts have been made to quantify and evaluate this rela-tionship in the field of retail activity. The object of this thesis is: 1) to develop a number of measures of re-tail accessibility; _{2) to evaluate the importance of} acces-sibility as a determinant of the volume of retail sales; and 3) to consider the significance of a sales potential concept based on retail accessibility.

Accessibility is measured by four methods which differ in the manner and extent to which they include the effects of competition and the effects of separation. In an empiri-cal test of these methods, accessibility ratings are derived for a set of new car dealers in the Boston area and those ratings are correlated with their annual sales. Results indicate that accessibility, by any method of measurement, is not the major determinant of the volume of sales. Limi-tations of the test case preclude a precise judgment of any particular method.

The characteristics of sales potential maps based on these methods are then considered; the nature of competitive accessibility ratings makes such sales potentials inherently unstable. Further research into the relationship between retail development and sales potential is required before the significance of a sales potential concept can be evalu-ated for planning purposes. In the field of market analysis, potential ratings may be of specific value.

Thesis Supervisor: Aaron Fleisher

Title: Associate Professor of Urban and Regional Studies

ACKNOWLEDGMENTS

The author is grateful to Professor Aaron Fleisher for his continued assistance and advice throughout this

study, and to Professor Lloyd Rodwin for his helpful sug-gestions concerning the manuscript.

This thesis would not have been possible without the generous assistance of the managers of several new car distribution agencies in Boston, who released confidential sales data to the author. Because of the nature of this information, no reference can be made to the names of those companies nor to the true locations of the salesrooms.

Automobile registrations were made available by Mr. Donald J. Laing of the Boston Record-American and Advertiser, and are gratefully acknowledged.

TABLE OF CONTENTS

Chapter

Page

ABSTRACT...---.----.-iii

ACKNOWLEDG NTS. ... 1

I. INTRODUCTION... - . 1

Potential Models--Retail Structure and Accessibility--Factors Determining

Sales Volume

II. MEASURES OF ACCESSIBILITY ... ... 8

Definition of Accessibility--Accessibility Formulae--Sales Potential--The Effect of

Separation--Zone Volume

III. EEPIRICAL TESTS...---16

Correlation--The Product--Procedure Figures 1-6

IV. ANALYSIS OF RESULTS...---.-29

Significance of Accessibility--Layout of Dealers--Accessibility to Population--The Parameters--Accuracy of the Results--Retail Zones

Figures 7-10

V. CONCLUSION . ... ... ..---. ----. 39

Sales Potential--Planning Significance--Marketing

VI. APPENDICES A. Competitive Accessibility... ... 45 Figure 11 B. Zone Centroida...49 Figure 12 C. Sample Calculation of Accessibility Contributions...53 D. Effect ofAgrgto...5 Figure 13

E. Unstable Sales Potential...58 Figure 14

PART ONE INTRODUCTION

The subject of accessibility has received wide consi-deration because of its presumed relationship to the spa-tial distribution of urban activities and to their inter-actions. Theoretical studies have focussed attention on the factors that underlie accessibility and on their in-fluence on locational decisions. For example, Mitchell and Rapkin have explored the interactions that characterize urban activities, and noted that each activity will attempt to maximize accessibility to the other activities to which it is linked.

Although its influence on urban development is consi-dered significant, there have been few attempts to define accessibility for the purpose of quantifying these rela-tionships and assessing their true significance. The work of Hansen, in defining accessibility and measuring its relation to residential growth, is of particular interest and will be referred to later.2 In the field of retail

1. Robert B. Mitchell and Chester Rapkin, Urban Traffic. A Function of Land Use (Columbia University Press, New York, 1954), Chapter VII.

2. Walter G. Hansen, "How Accessibility Shapes Land Use," Journal of the American Institute of Planners, Vol. XXV, No. 2, May 1959, p. 73.

-

-2-activity, although accessibility has long been an acknow-ledged factor, there are few methods available to quantify it and compare its influence with other factors.

The subject of this thesis is accessibility and its relation to retail sales. The investigation has three

ob-jectives: 1) to develop a number of measures of accessibi-lity at urban sites; 2) to evaluate the importance of accessibility in determining the volume of retail sales compared to other factors; and 3) to consider the signi-ficance of a sales potential concept for urban planning.

Potential Models

The concept that a location possesses a certain poten-tial for interaction due to the spapoten-tial distribution of potential interactors has been explored and developed by a number of social scientists. Stewart defined the possibi-lity of interaction with respect to an individual i

generated by population at

j

as:

V

=

k P' dij

Where Pj is the population at

j,

dij is the distance between i and

j,

and k is a constant of proportionality.3 _The

3. A number of potential models are compared and discussed in Gerald A. P. Carrothers, "An Historical Review of the Gravity and Potential Concepts of Human Interaction," Journal of the American Institute of Planners, Vol. XXII,

total possibility of interaction of an individual at i is the population potential at i, and is:

i V k P, + P 2 '' Pn

il i2 _in

Carrothers reports correlations between measures of poten-tial based on variations of this formula, and a number of phenomena such as migration, telephone calls, and traffic.4

In the field of retail activity, the major work along these lines was the development of a retail "gravitation" formula for inter-city trade. Reilly's "Law of Retail Gravitation" measures the attraction of two competing re-tail centers, for the trade of an individual somewhere in between them. According to this formulation, the distri-butions of purchases is given by:5

Ba

(Pa\

(Db\ 2

f~~ b_5bDa)

Where Ba and Bb are the proportions of an individual's trade attracted by two cities, a and b, respectively, Pa and Pb

are the populations of the cities; and Da and Db are the dis-tances from the individual to the cities. For intra-urban retail trade, there is no similar quantitative method to re-late the accessibility of retail sites with the level of ac-tivity at them.

4. Ibid., p. 98.

5. This formula was given extensive testing and the results are reported in P. D. Converse, "New Laws of Retail

Gravitation," Journal of Marketing (October, 1949), pp. 379-384.

3. 4 3.

-Retail Structure and Accessibility

Accessibility has long been recognized as a factor in the organization of retail land use. According to the theory of retail location, retail sites are allocated to various uses by the market process according to the compe-titive bids of merchants. The maximum rent bid of each merchant is determined by his estimate of income and

oper-ating costs at each site. The most important variables among the determinants of the maximum rent which any mer-chant can afford to pay for a site are the volume of sales and the markup. Both of these items, particularly the vol-ume of sales, are functions of location.6

For any site certain types of retail activity possess an inherent capacity to pay higher rents. Ratcliff states that this hierarchy of uses is not fixed, but depends on the location of the site:

Correctly defined, the hierarchy is not one of retail uses alone but of retail uses on appro-priate sites.... It should be further stated that for each site there exists a hierarchy of uses based on their rent-paying ability on that site, and that there is a hierarchy of sites based on differential productivities under the appropriate uses.

The advantage that location gives one site over another

6. Richard U. Ratcliff, The Problem of Retail Site Selec-tion (University of Michigan, Ann Arbor, 1939), p. 61. 7. Ibid., p. 73. (Italics his.)

-5-is the source of what Chamberlin terms the "monopoly income" of the landlord:8 "Two sites have different rents to the degree that they are in different markets..." The accessi-bility differences ,between sites and their effect on sales would appear largely responsible for the pattern and

dis-tribution of retail activity.

Factors Determining Sales Volume

A number of factory as well as accessibility will in-fluence the decision of a shopper when he chooses between alternative retail stores. The factors that determine sales volume can be considered in three groups: accessibi-lity, merchandising and agglommeration.

Accessibility: Buyers desire, among other things, to mini-mize the time and effort of shopping and a store will be

at an advantage, the closer it is to large volumes of shoppers. In addition, for each particular kind of store the purchasing habits of shoppers in the surrounding area are significant; a store selling expensive jewelry will require well-to-do clientele.

The number and location of competitors will also

affect the volume of sales; this will be considered in de-tail later. In general these factors refer to the location

8. Edward H. Chamberlin, The Theory of Monopolistic Com-petition (Cambridge, Harvard University Press, 1958), p . 268.0

of the site with regard to the location of purchasers and competing dealers and will be called, here, accessibility characteristics of the site.

Merchandising: In addition to the accessibility of the

site, there are a number of characteristics of the particu-lar store that will affect its volume of sales. The quality of the merchandise or service offered and the prices charged are extremely important. In addition, a number of intan-gibles will influence a potential customer's choice: the variety and selection available, the atmosphere of the

store, the courtesy of the employees, the advertising image, as well as the dealer's reputation for reliability and ho-nesty. These factors are subject to the policies and abili-ties of management and are called here merchandising char-acteristics of the store.

Agglomeration: Sales at a particular store are also influ-enced by the presence of nearby retail activities. If there are, in the immediate, area, other stores offering a variety of merchandise and services, the shopper is offered

an opportunity to make many purchases at the same time, and to combine several trips into one.

Similarly, if there are in proximity, a number of

stores that sell similar products, the buyer has the oppor-tunity to compare before making his purchase and to shop for the best buy. The advantages of agglomeration vary not

only with the nature and value of the product but also with the frequency of the purchase.

PART TWO

MEASURES OF ACCESSIBILITY Definition of Accessibility

As commonly used, the term accessibility does not have a precise meaning; it is usually thought of as a character-istic ofta site which is based on the amount and location of potential interactors. This characteristic is often considered a determinant of the location of different activities and of the level of activity occurring at these locations. In this thesis obly similar retail uses will be considered; consequently accessibility should be reflected in the level of activity

-the volume of sales - at different sites.

Accessibility is defined, for this thesis, as the relative volume of sales, at similar retail sites, due to the spatial distribution of potential interactors. For some types of prod-ucts the volume of purchases of an area may be influenced by

the abundance or lack of stores in the vicinity; the nature of the product and its substitutability are important. In the more usual case the effect of accessibility is largely in the distribution of trade. In the formulae derived below, the

zonal volume of purchases is assumed independent of accessibility. Accessibility formulae can be based on the potential model; the measurement of accessibility for residential areas by

9

Hansen is an example. By this method, accessiblity rating

9. Walter G. Hansen, "Accessibility and Residential Growth," unpublished L.2.P. thusis,

i.I.T.,

1959. Abbrief

-8--.

9-is the sum of "contributions" from zones, where eamh "contri-bution" represents the purchases of a zone at a certain site;

I = Vi F(jdj.)

where,jI± is the volume of purchases of zone i at site J, Vi is the size of zone i, F(jdi) is some function of the distance between zone i and site J, and k iB a constant of proportion-ality.

In the usual potential model, the same k is assumed for all the zones and since I is taken as a relative value, the

which is implied in each rating is simply left out. This accessibility rating only reflects the location of purchasers;

the number and location of other sites does not affect it. To vary the accessibility contribution and reflect competition the

factor ] must be evaluated.

It is also possible to defferentiate between accessi-bility formulae according to how they include the effect of

separation. In the simpler types a boundary is drawn around the site and the summation of all interactors within the boundary weighted equally, is the basis for all accessibility rating

of that site. The second type is similar to the potential models discussed, where many more zones are indluded, the

interactors weighted for separation according to some inverse power relationship.

- 10

-Accessibility Formulae

The different concepts of retail site accessibility will be the basis for four methods of measurement that

vary in their complexity and in the factors they include. They are: Method A is based on the distribution interactors around a site and weights all within a boundary equally; Method B also weights interactors within a boundary equally but reflects the location of competitors in drawing the boundary; Method C weights interactors according to their

distance, but does not reflect other competing sites; Method D weights interactors according to their distance and ac-counts for the location of competing sites.

To formulate these methods, imagine a region divided into zones a, b,....n, where Vi represents the size or volume of a zone. Sites A, B, ....M are the locations of dealers; i I is the accessibility rating of site J and is the sum of accessibility "contributions" from the zones;

I= Ia + _{+ .} InnIb

Method A: This is the simplest method; it sums up the volume of all zones within a specified radius of a site. All included zones are weighted equally, whether near the

site or the boundary; consequently the boundary is always somewhat arbitrary. The accessibility rating is:

I = Va + *... Vk

-11-Method B: In order to reflect competition in this method, boundaries are drawn equidistant from each site. Each in-teractor is counted only once and assigned to -the closest site. As in Method A, the weight of each zone is equal whether near boundary or adjacent to the site. The

acces-sibility ratin6 is:

JI= Va 4- Vb + ... k

(including all zones within the bounda5ry)

Method C: The accessibility "contribution" is weighted for distance, and the rating of a site is the sum of these

weighted "contributions"

I .LVa F(jda) + Vb F( b) + .... Vn F(jdn)

where F(jdi) is some inverse function of the separation be-tween site J and zone i. Since the weight of a zone's "con-tribution" to site J declines as the separation increases, the boundary problem should not be sinificant. In Method C, as in all potential models, the factor k, which should appear in each "contribution," is left out, because it is tacitly assumed to be the same for all zones. A rating derived in this manner is not in units of sales; it is really, J I

/

k whose units are those of VF(d). Since all k's are assumed equal, these ratings

can be used to proportion the total regional sales, without directly evaluating the factor k.

Method D: In Method D we assign a different value k to each zone. To evaluate ki consider the competitive situation at each zone. It requires that the sales made to that zone from all sites add up to the total zonal purchases:

-12-Solving for

1 _F(Adi)

+ F(Bdi) _{+ ... F( Md}

)

The accessibility contribution is then:

F(jd) Ii= k Vi F( 9d _Vi F)(=

F(Adi) + F(Bd ) . F(Md This states that the distribution of purchases from a zone i is based on the relative location of each site compared to the location of all the other sites around zone i. The accessi-bility rating of a site J, is then:

I= k..-Va F ( da _{J Jan} + k'-V F(idb) '''nVn F( d)

_{J n}

There is now a separate Ikfor each zone. Ratings derived by Method C will be equivalent to those of Method D only

for the special case when the factor k actually is the same 10

for each zone. Sales Potential

In the case of Method D, where iL is evaluated (and in Method B, where it is assumed equal to 1) the accessibility rating is in units of V. In Methods A and C, the accessibility ratings are in units of VF(d) and their absolute values

depend on the function F(d). Accessibility ratings

10. The way in which evaluating the factor & will reflect competition can be seen if one imagines a hypothetical

situation: in an urban area with sites A,B ... X, a new

dealer, Q, opens adjacent to one of the existing dealers. By Method C, which assumes all W's equal, the accessi-bility rating of a dealer is:

F

13-cannot be compared except when similarly derived.

If the merchandising and agglomeration characteristics of all dealers were the same, the accessibility rating would represent the relative level of sales at each site. To de-rive the sales potential at a site, jS, based on accessi-bility:

S x (total sales)

A BI .M

The Effect of Separation

The effect of separation on the probability of inter-action can be expressed in a number of ways. Potential mo-dels usually assume an inverse power relationship:

F( di)k

where x and k are constants; this type of relationship has been used to dist±'ibute urban travel between zones, although

I= VaF(jda) _{+ VbF( db) + -- VnF(d}

n

The existence of dealer Q does not affect any of the terms and therefore, has no effect on the accessibility rating of any site.

In Method D, the accessibility rating is: I = k aVaF( da) + kb F(db) + ... knVnF( _dn

The addition of a dealer Q adds a new term F (Q di) to the denominator of each k. and decreases its value. This will lower the value of gI. Some k's will be

af-fected more than others; if these zones which "con-tribute" most to

Z1I

are also most affected by the change

in k, I will be 7Aecreased by a significant amount. An exampli of the effect of site layout is given in Appendix A.

- 14

-other types have also been tried. The separation, d, is often approximated by distance or time. Its effect is

probably much more complicated, including the cost, comfort, and general effort expended in overcoming distance.

Zone Volume

To develop retail accessibility ratings, the "contri-butions" of zones have been summed for each site; each

"contribution" is a function of the volume of the zone. The volume of a zone can be expressed in several ways. For retail activity, however, the importance of any zone is re-lated directly to its volume of purchases. The units of V should be dollars, or if the purchases under consideration are homogeneous, simply units of that product.

The volume of purchases of a zone may often be approx-imated by other indices--income, number of households or even the population. These indices do not necessarily ex-press the volume of purchases; buying habits may differ for zones with similar indices. Therefore an accessibility rating based on these indices will approximate the true accessibility only as well as they approximate the volume of purchases.

11. For example: 1) Alan M. Voorhees, "Forecasting Peak Hours of Travel," Highway Research Board, Bulletft No.

203 (Washington, D. C., 195b); 2) 3. Douglass Carroll, Study Director, Chicago Area Transportation Study,

- 15

-The volume of purchases, V, has been assigned to a specific zone. In reality, purchasers move about the urban area and relating accessibility to their place of residence will not describe the true potential for interaction. For

certain types of sales, accessibility can more reasonably be related to places of employment, recreation, or some other activity.

PART THREE EMPIRICAL TESTS Correlation

The statistical test which is used in this thesis to evaluate the significance of accessibility in comparison with the other factors determining sales is the coefficient

12

of correlation. If accessibility were the only signifi-cant difference between stores the methods derived in the previous section would yield ratings that correlate

per-fectly with the actual sales; the coefficient of correla-tion would be one. On the other hand, if accessibility were unimportant, and sales variations were due only to merchan-dising and agglomerative differences between stores, the correlation would be zero. In reality sales are due to all three factors, and the correlation will probably be of some value other than zero or one. The coefficient of correlation

12. The coefficient of correlation is explained in any stan-dard text on statistics. For example, see: 1) Burring-ton and May, Handbook of Probability and Statistics

(Handbook Publishers, Inc., Sandusky, Ohio, 1953), Ch. XII; 2) R. A. Fisher, Statistical Methods for Research Workers (Oliver and Boyd, London, 1934), Ch. VI.

Briefly, r2 is the reduction in variance from the best linear regression line on x and y values:

r = coefficient of correlation r covariance of x and y

(standard deviation of x)(standard deviation of y)

-16-- 17

-can be used to calculate a factor, r, which indicates the reduction in the variation of sales among sites due to the assignment of accessibility ratings.

The Product

The empirical test of these formulae requires the loca-tion of a number of similar, competing stores. It is im-portant that the products they sell be similar, so that

ac-cessibility will be a valid basis for comparing sales'.

The main criterion for choosing a product was a prac-tical one--the availability of informativ n. Sales data is

jealously guarded information which merchants are reluctant to divulge. Just as important it was required to know the purchases of the product on a zonal basis. Another require-ment was that there be a limited number of competing dealers so that the calculations would be feasible by desk calcula-tor.

One product that met these requirements was new cars; new cars are registered according to the place of residence

of the purchaser and annual registrations were available for the Boston metropolitan area, by brand. Most important, the annual sales at Mletropolitan Boston dealers were re-leased to the author by the regional distribution agencies

of several companies.

Only one brand was used; the cars sold by these dealers are relatively homogeneous, although price, service and

advertising differences will affect the level of sales.

Some dealers were on "automobile row" while others were not, introducing varying agglomerative effects as well as mer-chandising, factors.

Procedure

The Boston metropolitan area was divided into approx-imately 100 zones, for which annual registration data was known. New car registrations of the brand under considera-tion were used as Vi, the volume of zone i. The zones were irregular in shape and coincided with cities and towns, ex-cept for the City of Boston, which was subdivided into 11 zones. The locations of 51 dealers were plotted on a map of the region. For 26 of these the annual sales were known, and accessibility ratings were calculated by the four

Methods. (Figure 1)

It was assumed that travel time represented the separa-tion as well as any simple index of separasepara-tion. Distances scaled from the map were converted into travel times by means of a graph (Figure 2) which relates travel time to

distance, depending on the type of facility used. The graph was made by the Boston College Seminar Research Bureau, and

is based on field surveys in the Boston Area conducted in 13

1959. The report also noted that for shopping trips,

13. Boston College Seminar Research Bureau, Travel in the Boston Region, Vol. II, February 1961, pp. 42-43.

-- 19

-LOCATION OF ZQES AND SITES FIGtE 1

BOSTON ITROPOLITAN APA

\CHELMSFO TEW UR \WH v

DR C TNORTH c ST

WEST OR D RE/ADONG DANVERS

BILLERICA * VE ERLY ACTON -\

I

I WEMCM /E M LE N G O6 NORTH % WESTON * RAMINGHAME LE - BO NATICK 7NEDA SH/N DEDHAM SERBORN DOVER L TO

HOLL TON RA NTRE

T TE CiZORWOO LISIG C N s NO EL 0-g jMEDAY \LI - -R- ₇ ~WALPOLE _AV

KTOON YG O HANOVER MARSHFIELD

I\ NORMNGOL $AONr

Zone Boundaries

Auto Dealer Sites *

Auto Dealer Sites for which accessibility

ratings were calculated and correlated with sales.*

*Note: The positions of sites indicated on this map are not those

of the Auto Dealers on which the empirical tests were made, but

Automobile Trip Travel Time* (By Type of Highway and Trip Length)

H4+44 -1 ! 11 1 +i 1

...

...

...

..

...

...

..

...

..

....

.

....

...

..

...

..

...

_1_1 12 4-4- _L _AH±fil . j ff 44Th I-Urban Arterial S ... . ... .. I T ' 4 4 t xpressways:--ti 44 - _IF .Downtown 1il -T I i f . 1 -4- 11 _q 4 rt7"_tr St -H44A reets -44 -rl-TTI 17 TTT I I TM _FTT F 144 4,.. _... -Hj , t4 4 it -i t.± ±

-mm

T E f 41- -- 4+ #4#4 -+- j" 1 4--2

4

6 8 10 12 14 16 18 20 22 24

* _{Graph taken from Studies of}

Urbcan Transportation,Vol.II,

Seminar Research Bureau, Boston College, (1561) p.4_2. TRAVEL TIME 60

50

0 4~0 30 E 20 10 0 DISTAiCE (miles)

fl I W I -H r! I I fl I lflElfl i I III I# . . . .T rii i i t T Ti

.. 4

. . . . ..... .......... . ...... ... ... 1 1 1 - , 1 1 . . . ... . . . I .. I --- Arterial, + j4-MIN FIGUI 2

3-5 minutes of terminal time is usually involved; conse-quently, 4 minutes were added to every value of travel time scaled from the graph.

The travel time used in these tests was calculated on-ly for auto travel, with normal driving conditions. This would appear reasonable for new car shopping trips which are probably made by car and in off-peak hours.

Method A: In Method A, the number of registrations within an arbitrary driving time of a site is counted. For this test a travel time of about 20 minutes was used correspon-ding to three miles. Within this boundary were a few whole zones and portions of several others. Proportions of the registrations of these zones on the boundary were assigned to a site, based on the proportion of the zone within the specified radius. Only rough proportions were possible, so the uniform three mile, radius was used without regard to time along routes.

The reduction of variance was----40% (Figure 3).

Method B: For Method B, the region was divided into market areas around each site; boundary lines were drawn perpen-dicular and equidistant between adjacent sites. Each pur-chaser is assigned to the closest dealer. In this case, as in Method A, fractions of zones were involved and as they could only be estimated roughly, boundary lines were located by distance rather than travel time along routes.

-- 22

-The reduction in variance was----43% (Figure 4).

Method C: In Method C, zones are weighted according to dis-tance, and the following formula was used to express that relationship:

F(jd )= 1 (.d&.) 2 JJ

Analyses of shopping trips have derived exponents for d ranging from 2.0 to 3.0. 1 The actual exponent is probably different for each product, as the effect of separation is not necessarily the same for every type of purchase. The exponent 2, though arbitrary, should give an indication of accessibility. The formula used was:

I Va + Vb +.... Vn

( d )2

_(Jdb)

2

With an inverse power function, the weight of a zone is dependent on its distance from a site. This distance was scaled from the centroid of the zone to the site and converted into travel time by the graph. When sites were within or adjacent to zones, the site-centroid distance is not accurate, and a different method was derived to calcu-late travel time for these cases.1 5

14. See: 1) J. Douglass Carroll, "Spatial Interaction and the Metropolitan Description," Papers and Proceedings of the Regional _{Science Association, Vol. 1, 1955; 2)} Boston College Seminar Research Bureau, op. cit.

15. This method gave a "typical" purchaser's driving time to the site based on the size and shape of a zone and

- 23

-The problem of boundaries, where to stop adding

additional zones to the summationshould not be critical; as distance increases, the weight, ( of each additional

zone decreases. In general, the cut-off point was extended where there were large zones, or where the density of sites was sparse.

The reduction of variance was----46% (Figure 5).

Method D: This method is the most complex. The procedure was to includ&,as in Method Cas many zones as would

con-tribute substantial amounts to sites under consideration.1 6 Then, the relative accessibility of each site around that zone was calculated. The "contribution" from zone i to site J is: 1

I -Vi (Jdi)2 and I= I + I

1 + 1 +J a

Jb-( d ) Jb-(

J

2

_(MdY

2

The reduction in variance was----32% (Figure 6).

the location of the site. It is. explained in Appendix

B.

16. The method of computation of an accessibility rating by methods C and D is shown, for a typical case, in Appendix C.

1200

900

600

300

CORRELATION OF ACCSSIBILITY AND SALES

100 200 300 400 500 600

CAR SALES

600 JillLfVJ [I (vehicles) III Jl -- ----. -- . -- . n a- f i llM - . . . ... Reduction in Variance _{I 43 I} -

-4

200 14 100 20 0 400

500-6

OAR SALE~S

160. eduction in

860.

Variance =46%I fltIi

I f I l l

r~~~~~

~ -- .. -. - - -- - - -- = -- - -. --1 2 .-- If -I r -0 --- .-. - ---.- 1200 40 rd -100 200 300 400 500 600 CAR SALES

400 Reduction in 4! 0 0it Il l [ l l t ] t 1 Yariance 32;--- -- tI .. . .=....-=.... --- _-.---.=- -- ,- rg - .-. l il. . . .

c

-e -1. -- .

2

- - I t --- ---- --- f[if

i

l l

a

,

w--

- =- m , ,

a

--

-

, -.-

--T---- - - --- ---. - - - - - - r - , ,' - - .e = - . a -.- 4 ,- -- -I - - -f--, . .- r . - ---- -- -- - I I. I 200 0- -100 100 200 300 400 500 600 CAR SALS

CORRELATION OF ACCESSIBILITY AND SALES

- 28

-PART FOUR ANALYSIS OF RESULTS

Significance of Accessibility

The results summarized are:

Reduction in variance--- A B C D 40 43 46 32

By any method, accessibility accounted for about 30 to 45% of the variation in new car sales from dealer to dealer. This appears quite high in view of all the merchandising and agglomerative factors that are usually imagined to play such a determining role.

For example, Ratcliff says, in discussing the signifi-cance of location in the customer purchasing habits for var-ious articles,1 7

...in the purchase of groceries, convenience to home is highly important because of the frequency

of purchase, bulk of the articles, relative unim-portance of comparison and the relative immediacy of the need.... On the other hand, the high eco-nomic value of an automobile, and the infrequency of purchase, result in attaching much less impor-tance to convenience of auto salesrooms...

The fact that auto sales are divided among a large num-ber of dealers in the metropolitan area reflects automobile

companies' belief that accessibility does count significantly in the volume. of sales. The existing distribution of auto salesrooms is a matter of company policy; exclusive fran-chises are given to each dealer for a specified area.

As the size of a salesroom increases, both merchandis-ing advantages and internal economies accrue to the dealer. he can offer a wider selection, his salesmen are more fully utilized, and so forth. These advantages of fewer, larger salesrooms do not increase indefinitely. With fewer deal-ers, the average customer must travel further to get to a salesroom. At some point the loss in customer convenience is more than the dealer advantage. The optimum number of outlets is dependent on the significance of accessibility as well as internal and merchandising characteristics. 8

Layout of Dealers

The similarity of values for Methods A, B, and C and especially the low value of Method D, were not expected.

As far as this study is concerned, the additional calculation involved in the more complex methods seems hardly justified.

18. This was pointed out to the author by the head of one of the regional distribution agencies who noted that the number of dealers in the Boston

metropol-itan area was to be reduced. Consumer demand has made a wider selection of models important for a

dealer, he stated, and at the same time, newer highways make each dealer convenient to a larger number of people than before.

-- 30

-The reason for this may lie in the special character of auto dealer locations. The layout of salesrooms is determined by the company to-eliminate any competing deal-ers in proximity. The layout over the region is fairly

uniform and the advantage of Method D, reflecting the effects of near-by competitive dealers, does not appear warranted by this situation. 9 In a more typical marketing situation where locations are freely chosen and dealers are sometimes near each other and sometimes far apart, Method D may yield higher correlations.

Accessibility to Population

Data on purchases of specific types not often available on a zone basis. To another index of zone volume, new values were calculated, substituting the populat

Pi, for new car registrations, Vi, of the The results were:

Reduction in Variance--- A B Vi 40 43 (Figures 7-10) _{Pi 40 34}

of products are see the effect of

of accessibility ion of a zone, particular brand. C D

46

32

45 39

The results are not very different; in all cases ex-cept Method D, the reduction in variance, with population as a measure of zone volume, is less than or about equal to the reduction in variance when vehicles were used. This

19. Appendix A shows how Methods C and D reflect the lay-out of dealers.

- 31

-was expected; in the derivation of these methods in Part Two, it was stated that other indices of zone volume will approximate the accessibility based on purchases only as well as these indices approximate the volume of purchases. The results indicate that, at the scale of zones used here, population is a reasonable basis for computing retail ac-cessibility for auto dealers-.

The Parameters

The parameters used in Methods A, B, C and D were cho-sen arbitrarily. To test the possibility of increasing the correlation with different parameters, new accessibil-ity ratings were computed for one case, Method D, using a closer cut-off point to cease adding zones. This is not the same as increasing the exponent but has a somewhat simi-lar effect by increasing the weight of closer zones.

D Dl' The results were---V 32 58

P 39 39

There is a marked improvement for Method D with vehicles, while with population, none at all. This test was not sufficiently clear to tell the effect of a different expo-nent.

Accuracy of the Results

Errors that are introduced by inaccuracies in measure-ment are difficult to estimate. In Methods C and D, distance

400 Reduction in 300 200 100 100 200 300 400 500 600 CAR SALE~S OF ACCESSIBILITY AND SALES

CORRELAT ION _YIGURE

200 Reduction in Variance

=

34 1.50 'I-i S100 ~50 100 200 300 400 500 600 CAR SALE~S

AACCLSSIBILITY AND SALES _{FIGUR a}

40 Cea=uenon 2.fl Va~riance 5 30 20 10

4zo

101003040 0 0 IA R 100 200 300 1400 500 600 CAR SALES

120 lecucnIon in -Variance=

39A

90 t enn 60 30 100 200 300 40o0

500

600 OAR SAES

OF ACCESSIBILITY AND SALES

- 36

-was scaled along mapped routes, using the shortest route observable. Where routes turned corners or curved a modi-fication was attempted. In- many cases, however, errors in reading and estimation accumulate and will yield inaccurate values of d. The problem of designating a route for travel time computation is also a source of error.. The four

curves in Figure 1 diverge sharply at large distances. As most routes involved portions of urban, suburban, express-way and occasionally downtown routes, visual estimation of

correct position between the lines introduces error. At large distances, where the curves are far apart, the error will be minimized because travel time enters the formula

as an inverse square; large absolute errors yield small differences in the weighting factor.

When the separation is small, however, errors are more significant and are likely to arise from the irregular shape of zones and non-uniformity within them. The size of zones is therefore a limit to the sensitivity of the formulae. Where zones are large, as in these tests, the methods of measurement may not give correct values for zones with near-by sites.2 0

20. An indication of this came when it was discovered that one site had been located on the map about 1Y2 miles from its true location. A recalculation was made (by Method D) for the corrected location and the change in accessibility rating was only about 10%.

- 37

-RETAIL ZONES

In this investigation, retail accessibility has been measured for sites and correlated with the sales volume at

these sites. It is also possible to, derive measures of re-tail accessibility for zones and to correlate accessibility ratings with the average level of sales at zones.

A correlation of this type, however, may tend to

exaggerate the influence of accessibility; individual site differences within each zone may balance out and their true significance will not be evident. For example, if retail sites are aggregated into zones, each zone will include some stores that, because of merchandising or agglomerative su-periority, sell more than other, equally accessible stores in the same zone. In averaging sales of that zone, the specific differences between stores may be lost. The aver-age sales per zone will not reflect fully merchandising and agglomerative factors; it will emphasize, rather, the com-mon characteristic of sites within that zone--their general location. If average zone sales are correlated with the .zone accessibility, the degree of correlation may not be the same as with a similar analysis for sites.

This is true of residential development as well. Each parcel has, in addition to its accessibility, other char-acteristics that influence its potential for development; environment, shape, building costs, and so on. The factor

of accessibility may not be the major influence in develop-ment of sites. When large numbers of parcels are

aggre-gated into zones, the difference between the average devel-opment potential of two zones, for reasons other than their location, will probably diminish.

It should be understood that the extent of correlation observed is dependent on the size of zones under considera-tion as well as on the influence of accessibility. As spa-tial aggregations include more individuals, the non-spaspa-tial characteristics of the individuals figure less in the zone's average potential. Only when zones are reduced in size to where they contain no more than one site, will the true im-portance of accessibility be evident.2 1

21. A hypothetical demonstration of the effect of aggrega-tion. is shown in Appendix D.

-- 39

-PART FIVE CONCLUSION

Sales Potential

The construction of potential maps to indicate the potential for manufacturing, distribution and other activi-ties raises the possibility of sales potential maps--con-tours showing the retail accessibility to purchasers at any point.22 To estimate anticipated sales of a hypothetical store would require further consideration of other factors that affect sales--merchandising and agglomeration--both for the hypothetical and existing stores; the potential map would give the spatial factor.

A potential map, based on competitive accessibility, however, would not be stable. Potential contouirson such a map will show accessibility ratings at any point in the

area for a hypothetical store. Since accessibility, accord-ing to this definition, is based on the location of other dealers as well as purchasers, the appearance of a new com-peting store will affect the accessibility of other loca-tions. If retail accessibility were defined in a more

22. For examples of potential maps, see:

1) Beverly Duncan and Otis Dudley Duncan, "The Measure-ment of Intra-City Locational and Residential Patterns,"

- 40

-limited way, as in Method C, the accessibility rating at any point would not be dependent on the location of dealers, and retail development at any location would have no effect on the potential contours.

It should be noted that with the appearance of a new store the sales potential changes in either case. With Method 0, however, the accessibility ratings do not change

and the effect is a uniform percentage decrease in the sales potential at every site.2 3 _{If the number of dealers in the}

area is large, this decrease may not be significant. In any case, the shape of the sales potential contours will not be changed, and comparative locational advantages will remain stable through time, as far as dealer changes are concerned.

In Method D, the shape of accessibility contours will be affected by each case of retail development. In this

Journal of Regional Science, Vol. 2, No. 2, 1960; 2) Edgar S. Dunn,, "The Market Potential Concept and

the Analysis of Location," Papers and Proceedings of the Regional Science Association, Vol. 2 (1956), p. 183.

23. _{From page13: J}

x (total sales) I _{+3I +'NI}

The addition of a new term, I, to the denominator of each site will decrease each .S by a factor of:

I+ I +I

+-- 41

-method, the decrease in sales potential with the opening of a new store is assigned to different locations according to their spatial relationship with the new store.2 4 _{Over time,}

relative accessibility advantages of locations will not re-main stable with retail development.

PlannSig Sificance

This thesis has not dealt directly with either the pro-cess or the pattern of retail development, but rather with what is felt to be an underlying cause--the relationship between accessibility and the volume of sales. The idea of guiding urban growth by the selective development of trans-portation facilities is only feasible where accessibility is a major determinant of land use. This investigation has shown that accessibility is not the major factor in deter-mining the volume of sales at new car dealers, and that wide variations in the sales and therefore rent paying ability are possible at any location.

Future research may establish certain categories of retail activity which are more dependent on accessibility. The development of these stores, however, would not neces-sarily tend towards any predictable pattern. With sales potential maps for particular types of retail activity,

a hierarchy of uses might be established for a set of sites, and thereby a hierarchy of sites for each use, all based

24. A hypothetical demonstratioh of the instability of a re-tail potential map based on Method D is shown in Appendix E.

- 42

-on the relati-onship between rent-paying ability and antici-pated sales.

If the distribution of sales is actually determined by competitive principles (similar to those of Method D), the sales potential pattern would be subject to unpredictable change, and the hierarchies based on these potentials might not be stable. For example, if a dealer opens at some loca-tion other than the optimum (by whatever criteria), he will not necessarily fail; he will merely earn less than he might have at some other location. His presence, however, will alter the sales potential at other locations, and the

optimum may now be in some other location. There may no longer be any point with sufficient sales potential to sup-port the entry of an additional store.

Just how significant this instability is over the long run, is quite important. If the decisions of private de-velopers have a predictable relationship to sales potential, then measurements of accessibility may be of some v4lue in anticipating developmental trends. Further research is needed in this area.

In any case, accessibility ratings may offer some means of quantitatively evaluating alternative plans by which pri-vate development is guided through land use controls. The problems of differentiating between retail uses for zoning purposes, as well as the criteria for such an evaluation, will require further study.

- 43

-Marketing

Although the planning possibilities of retail potential maps appear limited, it may be of specific value in

market-ing decisions, where the sales potential at a particular time and place is of interest. The usual method of estima-ting the sales of a proposed store is largely intuitive.25 The market analyst establishes a trading area from which the store is expected to draw its customers and then, based on the location of competing stores and the relative attrac-tion of the proposed store, he assigns a percentage of the

area's trade to the proposed store. All the factors that influence sales are weighted on the basis of the analyst's experience and judgment.

With the use of accessibility formulae, it should be possible to derive a rating for the spatial component of sales and allow the analyst to concentrate on rating the merchandising and agglomerative factors which require

sub-jective weighting.26 Additional investigation along these

25. For examples, see: 1) Richard L. Nelson, The Selection of Retail Locations (F. W. Dodge Corp., New York, 1958), p. 191; 2) Homer Hoyt, "Market Analysis of Shopping Centers," Urban Land Institute, Technical Bulletin No. 12, October 1949.

26. In Method D, for example, trade is distributed from a zone according to relative attraction of each site around it. If a rating, M, were assigned to each site which reflected its relative merchandising and

agglom-erative attraction, the formula could be modified to include its influence. Instead of basing the relative attraction on location, F(J d), as before:

- 44

-lines should be undertaken before the practical value of any accessibility formula can be evaluated.

P( di)

JIi =Vi F(Adi) + F(d) _BJi + ... F(Md )

The relative attraction of each site would depend on both the spatial attraction, F( di), and the non-spatial attrac-tion, JM:

JMF( i dj)

J

i

Appendix A

COMPETITIVE ACCESSIBILITY

Accessibility ratings will be calculated for two types of abstract dealer distributions by Methods C and D to il-lustrate the difference between a rating based solely on the location of purchasers and one which is based on the lo-cation of purchasers and competing dealers.

Assume a homogeneous plane of purchasers, who are in zones aa, ab...nn; the volume of each zone is Vi= 1. In the first layout, the dealers are located uniformly, one in each zone. (Figure lla) It is assumed that all merchan-dising and agglomerative characteristics are equal, and that sales will vary with accessibility. All transportation

routes are at right angles to the separation from any site to any zone is simply the sum of their horizontal and verti-cal separation. The inverse square relationship which

weights each zone according to its distance from the site is:

Distance F( d )

0 4 _{(For a site within a zone,}

1 1 intra-zonal distance

3 21 is assumed 1/2 unit.)

4 0

where F( d )

=a.2,

and the cut-off point at which J

i

ldistanceds(

zones are no longer added is 4.

-- 46 -COMPETITIVE ACCESSIBILITY a b C d e f FIQURE 11 a b c d ef g h i. - - * - * * * *! -- - ~ee-b d

e-1

e '

fh

g FIGUBE lla a .a . . a1 & a a 1* 1 6 In a a a b c d e f g h i FIGURE 11b

- 47

-Accessibility ratings will be calculated for the sites in two zbnes, dd and ff, by Methods C and D. (By inspection it is obvious that the ratings should be equal.)

4Method C: For the site in aa:

I=

nVii F( d. .)

aaI

;;Z a

ail

aaI (1)4 + (4)1 + (8).25 + (12).11

aa

=

11.32; Similarly, fI= 11.32. Method D: For the site in aa:

I

Z

h

Vii

P(aad ii)

aa _{E;aa "f F(} d) aa iiT 1a = (1). 4 + (4) 1 + (8) + (12) .11 aa 11.32 11.32 11.32 11.32 aaI = 11.32

=

1 aa 11.32 Similarly, fI= 1.

For the second layout, we again have a homogeneous plane of purchasers, but in this case, three of the stores have been moved out of zones ee, ef and fe, and are now located

in zone dd,' along with the original site in dd. Now acces-sibility ratings will be calculated for the store in ff and the original store in dd.

Method C: The accessibility rating in Method C is dependent upon only the location of purchasers, which has not changed. Therefore, the accessibility rating of the site in dd is the

- 48

-same as it wassbefore and is equal to the rating of ff.

Method D: For this case we will again consider any zone that is accessible to the site in ff or in dd, and distribute their

"contributions". For example, the "contributions" of zone ed to the sites in dd and ff are:

dded *078

)4 +)1+

(6).25 + (12).11~ 12.82

ff ed 12.82 _*009

Similarly, accessibility contributions are calculated for all zones that are accessible to dd or to ff. The new ratings of the sites in dd and ff are:

dd

dd ii

=

.802

ff ff Iii 1.249

Since the total number of stores has not changed from the first layout, these accessibility ratings are directly comparable to sales potentials. The new accessibility rating for the site in zone dd indicates that its sales potential has been reduced by 20% because of the increased competition.

On the other hand, the site in zone ff has increased its sales potential by about 25% because of fewer competitors in the vicinity.

Appendix B ZONE CENTROIDS

In Methods C and D, zonal "contributions" are weighted according to an inverse square function, , which varies with the travel time between Site J and zone i. In general, separation is measured from the site to the centroid

of a zone. This method, whereby the center of gravity is used to represent a "typical" individual, is reasonable for large travel times, where the travel time from the site to any point in the zone is not very different than the travel time to the center of gravity.

When a site is adjacent to or within a zone, the travel time from the site to the center of gravity will not be an accurate measure. This is most obvious when the site is at the center and travel time to the center of gravity is zero; this is clearly less than the travel time to a "typical" individual.

What is required is a new travel time, &, such that:

Vi F() V. F(d )

the zone volume, Vi, times the inverse square function of d is equal' to the summation of each individual times the function of his travel timeo d., to the site. In the case

of Methods C and D, the function is ,so it is required

-

-50-to find a d such that:

Vi =Vj 1

2 d 2

First assume a circular zone of radius R, with a uni-form density; the site is located in the center of the

2

zone. In this case Vi is tR and the travel time from any small circular element of length 2 7 r and width dr is equal to r + 4 (including terminal time); the equation is then:

Ir R2 1 2?r r dr 1

+ 4)2 ( + 4)

Integrating the expression and solving for

(r

+ 4): R

( + 4) _{(Log R+}

-

-4 R+i4

This expression has been evaluated and is plotted against values of R as a solid line. (Figure 12) With the same graph, zones which approximate semi-circles, (a), or sec-tors , (b), can be handled.

R

site sitit

(a) (b) (c)

For the common situation where a site is 6n or near the edge of a square-shaped zone, a combination of two

fig-- 51

-ures, (c) was assumed and (r + 4) evaluated for the combina-tion; this relationship is plotted as a dashed line on the graph. (Figure 12) All zones were assumed to be one or another of these shapes when a site was in or adjacent to them.

13 12

----

11If

i

a 0 9 r4 - 6 00 2 4 6 8 10 12

I IUS OF ZONE

(

minutes

)

travel

nce

time

s) (minutes)

A00ESSIBILITY CONTRIBUTION jIi

vehicles Vi

=

141 population Pi = 26,379

Method C Method D Method C Method D

() (2) (3) (4) (5) (6) (7) (8) (000) 20 2* 7 139 19,600 72 3,665 13,520 21 2.5 18 31 4,370 16 818 3,020 22 4.1 4 119 2,680 10 501 1,850 28 6.5 24 17 2,390 9 448 1,660 29 6.5 25 16 2,260 8 422 1,560 16 3.8 23 19 2,680 10 501 1,850 6 5.0 23 19 2,680 10 501 1,450 18 6.5 30 11 1,550 6 290 1,070

total 271 (9) total 141 total _26,380

* diameter of zone

(site within zone

(4) x 105 (3) ? 26) (5) = (4) x Vi (6): (4) xVi (97 (7) = (4) x Pi

(8)

=

x

Pi

(9)

SAMPLE CALCULATION OF ACCESSIBILITY _{CONTRIBUTION; Method 0 and Method R}

to site dista

(mile 7(jdi)

Appendix _D

EFFECT OF AGGREGATIONS

To evaluate effect of aggregation, the coefficient of correlation between accessibility and sales will be calcu-lated for a hypothetical set of sites, first, as individuals, and second, when aggregated into zones.

AN BM FX MM NM

4 1 2 3 1 3

C D GM H4M P

2

3

4

1

4

2

1= 1 1= 2 I=3

Consider a hypothetical portion of an urban area with twelve sites, A, B, ....

Q;

these sites have different merchandis-ing and agglomerative attractions which effect their level of sales. The numbers at each site, (EM), indicate the re-lative non-spatial attraction of each site due to these fac-tors. The accessibility of each site is dependent on the layout of sites and purchasers (or just purchasers, if Method C is used). Assume that, because of their similar location, the accessibility of sites A, B, C, and D is the

same and equal to 1 (a relative value), the accessibility